China's Great Leap Forward was inspired by the Soviet model. On the 40th anniversary of the October Revolution, in 1957, Khrushchev boasted that in fifteen years the Soviet Union would overtake the United States in industrial output. Mao responded by promising that China would surpass Britain as an industrial power in the same time. China and the Soviet Union competed for influence in the Third World.

Khrushchev's Third World strategy signalled a return to the Leninist idea of separate revolutionary paths. He supported anti-colonial nationalist movements - neglected by Stalin as part of the capitalist world - on the assumption that they might in time develop into socialist revolutions with vanguard Marxist parties of their own.

None of the leaders backed by Khrushchev (Nasser in Egypt and Syria, Nkrumah in Ghana, Sukarno in Indonesia) proved reliable clients, despite receiving huge transfers of military aid, industrial investment and technical advisers from the Soviet Union.

Only Cuba was a winning bet. With the overthrow of the Batista government in January 1959, the Kremlin began to give weapons to the Cuban revolutionaries. Soviet intelligence officers began to arrive in Havana. Washington became alarmed. Khrushchev might have been more cautious. He needed cuts in military spending to invest in the economy and could barely afford to antagonize the US. But he was provoked by the Americans, whose U-2 spy-planes were exposed when one of them was shot down in Soviet air-space. After the Americans attempted to overthrow the Castro government in the Bay of Pigs invasion in April 1961, Khrushchev began to deploy Soviet atomic warheads to Cuba, within striking distance of the United States.

He had overplayed his hand. The missiles were discovered by the US planes, and for thirteen days the world stood on the brink of a nuclear war, until Khrushchev climbed down and agreed to withdraw the missiles from Cuba in October 1962.